Ms. N. May   

Physics       Week 2(Sem. 2)      Name____________________________ 

Chapter Summary 

Electricity­Electric Fields 

Test Charge (qo) – An object with a very small magnitude of charge so as to not disturb the system.  It is used to determine the extent to which surrounding charges generate a force. 

Electric Fields 

The electric field (E) is the force per Coulomb, F/qo, experienced by a test charge in the presence of other charged object(s).  Through this definition it should be clear that the electric field is a vector quantity that points in the same direction as the electric force for positive point charges.  The force and field point opposite for a negative point charge.  It is the surrounding charges that create an electric field at a given point.  All surrounding charges contribute to the net electric field.  To determine the net electric field it is necessary to determine all of the individual electric fields and then find the vector sum. 

Point Charges 

Point charges are used to determine the electric field around electrically charged objects because the equations simplify.  If Coulomb’s law is considered using qo for the point charge and q for the charge in question the equation becomes 

 

In the above equation divide both sides by q0 to get 

     

This shows how the charge of the point charge is not needed to determine the field experienced by a charge.  Often symmetry in problems will prove to simplify the solution and provide useful information. 

Electric Field Lines 

Since electric charges create electric fields in the space surrounding them it is useful to have a map that gives the directions and magnitudes of all of the electric fields present at different locations.  Michael Faraday set up an experiment that determined electric field lines point radially outward from a positive charge.  The electric field lines were found to point radially inward toward negative charges.  This makes sense in the opposites attract and opposites repel.  The field lines are found 360 degrees around the charge, however only some are drawn to eliminate confusion.  The amount of field lines indicates the strength, so a point with 5 times the number of lines than a point with charge +q would indicate a charge of +5q.  The pattern of electric field lines also indicates the magnitude or the strength of the field.  When field lines are close together that would indicate a stronger field strength.  When the field lines are further spaced apart, further from the center of charge, the field strength is weaker. 

Electric Dipoles 

Often electric field lines are curved, as in the case of electric dipoles.  A dipole consists of two electric charges of equal magnitude but opposite sign.  The electric field of a dipole is proportional to the product of the magnitude of one of the charges and the distance between the charges (called the dipole moment).  The pattern of the lines for the dipole indicates that the electric field is greatest in the region between and immediately surrounding the two charges, since the lines are closest together there.  For any given field line, it originates at the positive charge and ends on the negative charge.  In general, electric field lines always begin on a positive charge and end on a negative charge and do not start or stop in midspace.  Furthermore, the number of field lines leaving a positive charge or entering a 

Ms. N. May   

negative charge is proportional to the magnitude of the charge.  So if 100 field lines were drawn out of a +4q charge, then 75 would be drawn for a +3q charge and 25 for +q.  For two identical charges the electric field lines are curved.  For two positive charges, there is an absence of field lines between the charges, this indicates a weak field directly between the charges.  When drawing electric field lines be sure that they never cross over one another, they can never be crossed. 

The Parallel Plate Capacitor 

The equation for the electric field of a point charge can be reevaluated using calculus to be derived for point charges distributed over a surface.  One example of this is the charge and electric field on a parallel plate capacitor.  Each plate has an area, A, with one plate having a charge of +q and the other a charge of –q.  The charges are spread uniformly across the area of the plate.  In the region between the plates and away from the edges, the electric field points from the positive plate toward the negative plate and perpendicular to both.  Gauss’ law can be used to show the magnitude of the electric field, it says  

 

Sigma (σ) denotes the charge per unit area (q/A) of the plate, also called the charge density.  The field has the same value at all places between the plates, except by the edges.  Note the field does not depend on the distance of the charges from the plates, whereas the isolated point charge does depend on distance. 

Potential Energy 

Electric potential energy is analogous to gravitational potential energy.  If a point charge, +qo, were placed between two oppositely charged plates.  The force experienced by the point charge, F=qoE, would be directed toward the negative plate.  Therefore the 

work done by the electric force equals the difference between the electric potential at A and that at B: 

 

The Electric Potential Difference 

Since the work done depends on the charge q0, the work is usually expressed per unit charge.  The equation becomes: 

 

Electric potential is the electric potential energy of a small test charge divided by the charge itself.  The equation for the electric potential, V, is defined as 

 

Where the electric potential (V) is in units of Joules (EPE) per Coulomb (q0), or J/C which is called the volt. 

The electric potential can be related to the work equation 

∆  

Neither the electric potential nor the potential difference can be determined for one value, but rather only the differences can be determined. 

As a positive point charge, q0, accelerates from an area of higher electric potential to an area of lower electric potential in the direction of the oppositely charged plate.  If a point charge of –q0 were to be in the same electric field it would accelerate in the opposite direction, toward the other plate.  Therefore a negative charge accelerates from an area of lower electric potential energy to an area of higher electric potential. 

 

   

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N. May ABC Math Week 2

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A) B)

C) D)

1. Which diagram best represents the electric field arounda negatively charged conducting sphere?

2. In the diagram below, A is a point near a positivelycharged sphere.

A) B) C) D)

Which vector best represents the direction of theelectric field at point A?

A) B)

C) D)

3. Which diagram best represents the electric fieldsurrounding a positive point charge?

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A) B) C) D)

4. Which graph best represents the relationship between the magnitude of the electric field strength, E, arounda point charge and the distance, r, from the point charge?

5. The diagram below shows the arrangement of threecharged hollow metal spheres, A, B, and C. The arrowsindicate the direction of the electric forces actingbetween the spheres. At least two of the spheres arepositively charged.

A) sphere A B) sphere B

C) sphere C D) no sphere

Which sphere, if any, could be negatively charged?

Base your answer to the following question on theinformation and diagram below.

Two small metallic spheres, A and B, are separatedby a distance of 4.0 × 10–1 meter, as shown. The chargeon each sphere is +1.0 × 10–6 coulomb. Point P islocated near the spheres.

A) B)

C) D)

6. Which arrow best represents the direction of theresultant electric field at point P due to the charges onspheres A and B?

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7. In the diagram below, P is a point near a negativelycharged sphere.

A) B)

C) D)

Which vector best represents the direction of theelectric field at point P?

A) Both forces are attractive.

B) Both forces are repulsive.

C) The gravitational force is repulsive and theelectrostatic force is attractive.

D) The gravitational force is attractive and theelectrostatic force is repulsive.

8. Two positively charged masses are separated by adistance, r. Which statement best describes thegravitational and electrostatic forces between the twomasses?

9. Two equal positive point charges, A and B arepositioned as shown below.

A) A B) B C) X D) Y

At which location is the electric field intensity due tothese two charges equal to zero?

Base your answer to questions 10 and 11 on thediagram below which represents two small chargedspheres, A and B, 3 meters apart. Each sphere has acharge of +2.0 × 10–6C.

A) into the page B) out of the page

C) toward the left D) toward the right

10. If a positive charge is placed at point x, the directionof the net force on the charge will be

A) B)

C)

D)

11. Which diagram best illustrates the electric fieldbetween charges A and B?

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12. In the diagram below, two positively charged spheres, A and B, of masses mA and mB are located a distance dapart.

A) B)

C)

D)

Which diagram best represents the directions of thegravitational force, Fg , and the electrostatic force, Fe ,acting on sphere A due to the mass and charge ofsphere B? [Vectors are not drawn to scale.]

A) stronger and repulsive

B) weaker and repulsive

C) stronger and attractive

D) weaker and attractive

13. Two protons are located one meter apart. Compared tothe gravitational force of attraction between the twoprotons, the electrostatic force between the protons is

Base your answer to the following question on thediagram below which represents two small, chargedconducting spheres, identical in size, located 2.00meters apart.

A) B)

C) D)

14. Which diagram best represents the electric fieldbetween the two spheres?

Base your answer to questions 15 and 16 on thediagram below which represents two charged spheres, X and Y.

A) decrease B) increase

C) remain the same

15. Moving the two spheres toward each other wouldcause their electrical potential energy to

A) B) C) D)

16. Which arrow best represents the direction of theelectric field at point A?

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A) B)

C) D)

17. Which diagram best illustrates the electric field aroundtwo unlike charges?

18. An electron is located in the electric field between twoparallel metal plates as shown in the diagram below.

A) positively, and the electric field is directed fromplate A toward plate B

B) positively, and the electric field is directed fromplate B toward plate A

C) negatively, and the electric field is directed fromplate A toward plate B

D) negatively, and the electric field is directed fromplate B toward plate A

If the electron is attracted to plate A, then plate A ischarged

Base your answer to questions 19 through 21 on thediagram below which represents a voltage sourceconnected to two large, parallel metal plates. Theelectric field intensity between the plates is 3.75 × 104

Newtons per coulomb.

A) decrease B) increase

C) remain the same

19. If the source is replaced with one having twice thepotential difference and the distance between theplates is halved, the electric field intensity between theplates will

A) 9.38 × 105 V B) 4.00 × 103 V

C) 3.75 × 102 V D) 1.50 × 102 V

20. What is the potential difference of the source?

A) decreases B) increases

C) remains the same

21. As a proton moves from A to B to C, the electric forceon the proton

22. An electron is placed between two oppositely chargedparallel plates as shown in the diagram below.

A) decreases B) increases

C) remains the same

As the electron mover toward the positive plate, themagnitude of the electric force acting on the electron

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Base your answer to questions 23 and 24 on thediagram below which shows two parallel metal plates A and B connected to a voltage source.

A) 200. eV B) 250. eV

C) 500. eV D) 1,000 eV

23. If an object carrying a charge of 2 elementary chargesstarts from rest at plate A and is accelerated to plate B by the electric field, the total work done by theelectric field on the object is

A) decreases B) increases

C) remains the same

24. As a charged object moves from plate A to plate B, theelectric force on the charged object

25. The diagram below shows a point, P, located midwaybetween two oppositely charged parallel plates.

A) travel at constant speed toward the positivelycharged plate

B) travel at constant speed toward the negativelycharged plate

C) accelerate toward the positively charged plate

D) accelerate toward the negatively charged plate

If an electron is introduced at point P, the electron will

Base your answer to the following question on theinformation and diagram below.

Two parallel plates separated by a distance of 1.0 × 10–3 meter are charged to a potential difference of12 volts. An alpha particle with a charge of +2elementary charges is located at point P in the regionbetween the plates

A) accelerate toward the positive plate

B) accelerate toward the negative plate

C) move at constant speed toward the positive plate

D) move at constant speed toward the negative plate

26. The electric field between the plates will cause thealpha particle, starting from rest at point P, to

Base your answer to questions 27 and 28 on thediagram below which represents two large parallelconducting plates charged to a potential of 10. volts.The plates are separated by a distance of 0.050 meter.

A) into the page

B) out of the page

C) toward the top of the page

D) toward the bottom of the page

27. If an electron were projected into the electric fieldwith a velocity v, it would experience a deflection

A) A B) B C) C D) D

28. The direction of the electric field at point P is towardpoint

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29. A moving electron is deflected by two oppositelycharged parallel plates, as shown in the diagrambelow.

A) A to B B) B to A C) C to D D) D to C

The electric field between the plates is directed from

30. A positive test charge is placed between an electron, e, and a proton, p, as shown in the diagram below.

A) A B) B C) C D) D

When the test charge is released, it will move toward

31. A beam of electrons is fired from point A toward plate B as shown in the diagram.

A) speed up

B) slow down

C) be pushed up

D) be pushed toward the right

After the beam passes through a hole in positivelycharged plate B, the electrons will

A) less, and in the same direction

B) less, but in the opposite direction

C) greater, and in the same direction

D) greater, but in the opposite direction

32. A proton and an electron traveling with the samevelocity enter a uniform electric field. Compared tothe acceleration of the proton, the acceleration of theelectron is

33. Two plastic rods, A and B. each possess a net negativecharge of 1.0 x 10–3 coulomb. The rods and apositively charged sphere are positioned as shownbelow.

A) B)

C) D)

Which vector best represents the resultant electrostaticforce on the sphere?

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34. The diagram below represents oppositely chargedplates in an evacuated glass tube.

A) B)

C)

D)

Which diagram below represents the path of freeelectrons between the charged plates?

Base your answer to the following question on thediagram below which represents an electron beingprojected between two oppositely charged parallelplates.

A) into the page B) out of the page

C) to the right D) to the left

35. In which direction will the electric field deflect theelectron?

A) decreases B) increases

C) remains the same

36. An electron is located between a pair of oppositelycharged parallel plates. As the electron approaches thepositive plate, the kinetic energy of the electron

A) coulombs per joule

B) coulombs per newton

C) joules per coulomb

D) newtons per coulomb

37. Gravitational field strength is to Newtons per kilogramas electric field strength is to

A) 8.35 × 1024 N B) 1.67 × 105 N

C) 3.20 × 10–14 N D) 1.67 × 10–14 N

38. What force will a proton experience in a uniformelectric field whose strength is 2.00 × 105 Newtons percoulomb?

39. The diagram below, which illustrates the Millikan oildrop experiment, shows a 3.2 × 10–14 -kilogram oildrop with a charge of-1.6 × 10–18 coulomb. The oildrop was in equilibrium when the upward electricforce on the drop was equal in magnitude to thegravitational force on the drop.

A) 2.0 × 10–5 N/C B) 2.0 × 105 N/C

C) 5.0 × 10–5 N/C D) 5.0 × 105 N/C

What was the magnitude of the electric field intensitywhen this oil drop was in equilibrium?

A) unchanged B) doubled

C) halved D) quadrupled

40. A charged particle is placed in an electric field E. Ifthe charge on the particle is doubled, the force exertedon the particle by the field E is

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A) 10 N/C B) 1.6 × 10–19 N/C

C) 6.3 × 1018 N/C D) 9.1 × 10–31 N/C

41. What is the magnitude of the electric field intensity ata point in the field where an electron experiences a1.0-newton force?

Base your answer to the following question on thediagram below which shows two large parallel metalplates connected to a source of electric potential. Theplates are 4.0 × 10–3 meter apart and the potentialdifference across the plates is 100 volts.

A) decreases B) increases

C) remains the same

42. As an electron moves from plate B toward plate A, theelectric force on the electron

A) 10 C B) 2.0 C C) 0.2 C D) 0.1 C

43. What is the charge on an object that experiences aforce of 5 Newtons in an electric field of 50 Newtonsper coulomb?

A) 1.3 × 1023 V B) 2.0 × 101 V

C) 2.0 × 107 V D) 5.0 × 10–2 V

44. A distance of 1.0 × 103 meters separates the charge atthe bottom of a cloud and the ground. The electricfield intensity between the bottom of the cloud and theground is 2.0 × 104 Newtons per coulomb. What is thepotential difference between the bottom of the cloudand the ground?

A) 3.68 × 10–44 N/C B) 1.44 × 10–6 N/C

C) 3.68 × 106 N/C D) 1.44 × 1044 N/C

45. What is the magnitude of the electric field intensity ata point where a proton experiences an electrostaticforce of magnitude 2.30 × 10–25 newton?

46. The diagram below represents an electron within anelectric field between two parallel plates that arecharged with a potential difference of 40.0 volts.

A) 3.20 10–34 N/C B) 2.00 10–14 N/C

C) 1.25 104 N/C D) 2.00 1016 N/C

If the magnitude of the electric force on the electron is2.00 ×10–15 newton, the magnitude of the electric fieldstrength between the charged plates is

A) 1 V B) 20 V

C) 0.05 V D) 400 V

47. If 20 joules of work is used to transfer 20 coulombs ofcharge through a 20-ohm resistor, the potentialdifference across the resistor is

A) 0.25 joule B) 9 joules

C) 36 joules D) 4.0 joules

48. The work required to move a charge of 3.0 coulombsthrough a potential difference of equal to 12 volts is

A) 45 V B) 15 V C) 3.0 V D) 5.0 V

49. If 15 joules of work is required to move 3.0 coulombsof charge between two points, the potential differencebetween these two points is

A) 0.67 V B) 2.0 V

C) 3.0 V D) 1.5 V

50. Moving a point charge of 3.2 × 10–19 coulomb betweenpoints A and B in an electric field requires 4.8 × 10–19

joule of energy. What is the potential differencebetween these two points?

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A) 1.6 × 10–9 V B) 4.0 × 10–3 V

C) 2.5 × 102 V D) 1.0 × 1014 V

51. Moving 2.5 × 10–6 coulombs of charge from point A topoint B in an electric field requires 6.3 × 10–4 joules ofwork. The potential difference between points A and Bis approximately

A) 6.0 V B) 0.33 V

C) 3.0 V D) 12 V

52. If 6.0 joules of work is done to move 2.0 coulombs ofcharge from point A to point B. what is the electricpotential difference between points A and B?

A) 1.6 × 10–21 J B) 1.6 × 10–19 J

C) 1.6 × 10–17 J D) 1.0 × 102 J

53. How much work is required to move a single electronthrough a potential difference of 100. volts?

54. The graph below shows the relationship between thework done on a charged body in an electric field andthe net charge on the body.

A) power

B) potential difference

C) force

D) electric field intensity

What does the slope of this graph represent?

A) 1.0 V B) 1.6 × 10–19 V

C) 9.0 × 109 V D) 6.3 × 1018 V

55. If 1.0 joule of work is required to move a charge of 1.0coulomb between two points in an electric field, thepotential difference between these two points is

A) 1.0 × 100 V B) 9.0 × 109 V

C) 6.3 × 1018 V D) 1.6 × 10–19 V

56. If 1.0 joule of work is required to move 1.0 coulombof charge between two points in an electric field, thepotential difference between the two points is

A) 100 volts B) 25 volts

C) 0.25 volt D) 4.0 volts

57. If 20.0 joules of work is needed to move 5.0 coulombsof electrical charge through a circuit, the voltage is

A) 60. V B) 30. V C) 15 V D) 2.5 V

58. Moving 2.0 coulombs of charge a distance of 6.0meters from point A to point B within an electric fieldrequires a 5.0-newton force. What is the electricpotential difference between points A and B?

A) 5.0 V B) 2.0 V

C) 0.50 V D) 0.41 V

59. In an electric field, 0.90 joule of work is required tobring 0.45 coulomb of charge from point A to point B. What is the electric potential difference betweenpoints A and B?

60. The diagram below shows proton P located at point A near a positively charged sphere.

A) 6.4 × 10–19 V B) 4.0 × 10–19 V

C) 6.4 V D) 4.0 V

If 6.4 ×10–19 joule of work is required to move theproton from point A to point B, the potentialdifference between A and B is